Question

solve a variety of percent problems
when solving problems involving percents, it is important to understand how
to use the given information. a general guideline for writing equivalent ratios
for these types of problems is shown below.
\\(\frac{\text{part}}{\text{whole}} = \frac{\\%}{100}\\)
to solve each problem, substitute the given information into the appropriate
place.

what percent of 125 is 75?
a. set up equivalent part - to - whole ratios.
\\(\frac{\text{part}}{\text{whole}} = \frac{\\%}{100}\\) | \\(\frac{75}{125} = \frac{\blacksquare}{100}\\) | \\(75\div1.25 = 60\\)
\\(75\\) is \\(60\\%\\) of \\(125\\).

in a class, 10 students like salad. if \\(40\\%\\) of the students like salad, how many
students are in the class?
b. set up equivalent part - to - whole ratios.
\\(\frac{\text{part}}{\text{whole}} = \frac{\\%}{100}\\) | \\(\frac{10}{\blacksquare} = \frac{40}{100}\\) | \\(100\div4 = 25\\)
\\(25\\) students are in the class.

1. in a student council election, kyle receives 120 votes for president. if kyle

receives \\(60\\%\\) of the votes, how many students vote in the election?

1. in a school, 105 students are sixth graders. if \\(35\\%\\) of the students in the

school are sixth graders, how many students are there in the school?

1. the polar exhibit at a zoo has only penguins and seals. there are

14 penguins for every 6 seals. what percent of the exhibit is seals?

1. redfield, new york is one of the snowiest places in the united states,

with an average annual snowfall of 22 feet. so far this year, redfield has
received 105.6 inches of snow. what percentage of redfield’s average
annual snowfall has fallen in redfield so far?

Explanation:

Problem 1:

Step1: Identify part, whole, and %.

Part = 120 (votes Kyle received), % = 60, Whole =? (total voters)
Use the formula $\frac{\text{part}}{\text{whole}}=\frac{\%}{100}$

Step2: Substitute values into the formula.

$\frac{120}{\text{whole}}=\frac{60}{100}$
Cross - multiply: $60\times\text{whole}=120\times100$

Step3: Solve for whole.

$\text{whole}=\frac{120\times100}{60}=200$

Step1: Identify part, whole, and %.

Part = 105 (sixth - graders), % = 35, Whole =? (total students)
Use the formula $\frac{\text{part}}{\text{whole}}=\frac{\%}{100}$

Step2: Substitute values into the formula.

$\frac{105}{\text{whole}}=\frac{35}{100}$
Cross - multiply: $35\times\text{whole}=105\times100$

Step3: Solve for whole.

$\text{whole}=\frac{105\times100}{35}=300$

Step1: Find the total number of animals.

Number of penguins = 14, Number of seals = 6. Total number of animals = 14 + 6 = 20

Step2: Identify part and whole for seals.

Part (seals) = 6, Whole (total animals) = 20
Use the formula $\frac{\text{part}}{\text{whole}}=\frac{\%}{100}$

Step3: Substitute values into the formula.

$\frac{6}{20}=\frac{\%}{100}$
Cross - multiply: $20\times\%=6\times100$

Step4: Solve for %.

$\%=\frac{6\times100}{20}=30$

Answer:

200 students vote in the election.

Problem 2: